# Four-Point Parabolas

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Isaac Newton explicitly constructed four-point parabolas in *Arithmetica Universalis* (1707). In this Demonstration, you can drag four points that define two parabolas most of the time. By Sylvester's four-point theorem, the points form a concave set with odds 25/36. The corners of a rectangle also cannot be on a parabola. The precise odds that four random points can define a parabola appears to be an unsolved problem.

Contributed by: Ed Pegg Jr (August 2020)

Open content licensed under CC BY-NC-SA

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